BankBoston Corp. agreed to buy Robertson Stephens & Co. from BankAmerica Corp. for about $800 million, paying a premium price for one of the top names in high-technology capital raising.

The purchase gives BankBoston, which has been regarded as vulnerable to a takeover, added prestige and something that only a few larger banks have: a full-fledged investment bank, including lucrative stock-underwriting and merger-advisory...